Why is "You’ve brought a knife to a gun fight" considered to be a mixed metaphor?

To understand the mixed metaphor in this case, I believe you need to expand the scope of the article you are interested in (emphasis mine):

If anything, you are underthinking this, perhaps dangerously so.

You’re uncomfortable with the communication; you don’t want it; you don’t buy his rationale for it; you have indicated by typical “polite” means — asserting your commitment to your marriage then ignoring his texts and calls — that you aren’t receptive to his attention; and he is running through these red lights as if they aren’t even there.

Even in the rosiest of interpretations, his actions point to a person who is operating outside the norms of healthy behavior.

You, however, are trying your best to stay within them — and flustered that it hasn’t worked. Pardon the mixed metaphor, but you’ve brought a knife to a gunfight.

The author has used two unrelated metaphors to describe the same situation: one to describe the man's behavior, and another to describe the woman's. Though this doesn't produce "a ridiculous effect" as required by the definition of "mixed metaphors", and the author's use does make this confusing, since the metaphors are two paragraphs apart, I do believe this is the author's intent.

It's not a 'mixed-metaphor'. The knife/gun example doesn't fit the definition. I believe the author is simply mistaken.

A mixed metaphor, as defined by the Oxford Pocket Dictionary of Curent English (2009) is:

n. a combination of two or more incompatible metaphors, which produces a ridiculous effect (e.g., this tower of strength will forge ahead).

There are not two metaphors in your example. That is why I think the author you quoted is mistaken.